The debate over NHS privatisation has been reignited just months before the general election as the first private healthcare operator to run an NHS hospital trust has announced it is pulling out of the deal.

Circle Holdings said it was "no longer sustainable" to keep running the Hinchingbrooke healthcare trust in Cambridgeshire due to funding cuts and pressure on its A&E department. The firm said it had pumped in nearly £5 million to prop up Hinchingbrooke, meaning it would have the right to terminate the franchise.

Senior politicians have fought to pin the blame for giving Circle the contract to run Hinchingbrooke on their rivals, with shadow health secretary Andy Burnham insisting that that "there's no debate about it... the coalition appointed Circle".

.@patrickwintour There's no debate about it, Patrick: the Coalition appointed Circle. Their NHS policy is unravelling before our eyes.

He told MPs: "In fact, the Shadow Health Secretary, sitting there demurely, is the only man in England who has ever privatised an NHS hospital, and they dare to lecture us. Hinchingbrooke hospital – the only NHS hospital to be privatised, and by the Labour party."

Burnham insisted it was a "distortion of his record" as he said there was still an NHS bidder in contention for the contract before the coalition signed it. But a Circle spokesman said that "it was clear by the end of 2009 [when Burnham was health secretary] that Hinchingbrooke would be run by a private company".

In a statement, the shadow health secretary said ministers needed to reassure patients and set out a plan for the hospital's services to continue as Circle seeks to exit its contract.

“The government were explicitly warned two years ago about the risky business model Circle were operating, but failed to take any action. Given that these risks were known at the outset, Ministers must explain why they judged Circle a safe choice to run this hospital. They must also set out today how long they have known about the problems at Hinchingbrooke," he added.

Circle said there had been unprecedented increases in accident and emergency attendances, a lack of care places for patients awaiting discharge and that funding had been cut by 10.1% this financial year.

The company said these conditions had "significantly worsened in recent weeks". It has already pumped £4.84 million into the trust and would be "highly likely" to have to make further support payments that would breach the £5 million cap, it said.

It also said it was facing an imminent report from the Care Quality Commission (CQC) which it expected to be "unbalanced".

Circle began operating Hinchingbrooke in February 2012, the first time the management of an NHS trust had been delegated to a private company. At the time, unions warned that its management of Hinchingbrooke was an "accident waiting to happen".

However Circle warned in August that changes to funding mechanisms had left "uncertainty over Hinchingbrooke's profitability over the next year" though it said its "patient-centred and innovative approach should ensure the long-term sustainability of the contract". But it spelled the end of the venture in a statement today.

It said: "Circle today announces that it has determined that its franchise to operate Hinchingbrooke Health Care NHS Trust is no longer sustainable under current terms and that it has entered into discussions with the NHS Trust Development Authority (TDA) with the view to ensuring an orderly withdrawal from the current contract."

Circle defended its running of the hospital, saying that it had been transformed since the 2012 takeover when it was described as a "basket case" facing closure.

It said it had invested in the quality of care, in staff and facilities and won a number of awards, while meeting key measures including low mortality rates, "excellent" patient feedback and waiting time targets.

Local MP Jonathan Djangoly, who represents Huntingdon, said that Circle's decision was "a shock and a shame" but complained that unions and other critics of privatisation had used the hospital as a "political football".

"Hinchingbrooke is a well-loved local small district hospital. It had 15 years of constant closure threats and then Circle took over and it seemed like we had stability and an excellent management system," he told BBC Radio 4's Today.

"They revolutionised staff relations, they empowered staff, they invested in the infrastructure and what was a very average service became, in many ways, excellent."

However, Peter Carter, general secretary of the Royal College of Nursing, said: "This is deeply worrying news for staff and patients and further highlights the major financial crisis facing the NHS, and the daily pressure facing staff.

"Hinchingbrooke was one of the first NHS hospitals to be taken over by a private provider and at the time many considered this kind of arrangement to be the way forward for the health service. This announcement shows that private sector involvement is not always the answer.

"This news also highlights just how much pressure is being managed by NHS trusts around the country who are struggling to keep up with patient demand while remaining financially secure.

"Every effort must now be made to support staff to continue providing high quality patient care."